A third-grade class has 12 girls and 13 boys. A fourth-grade class has 10 boys and 11 girls. When picking teams for PE, one captain will make a selection from the fourth-grade class, then the other captain will make a selection from the fourth-grade class. After that, the first captain will make a selection from the third-grade class, and the second captain will do likewise. Assuming everyone has an equally likely chance of being selected, what is the probability that the first captain will pick two girls before picking any boys?
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